Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127. Show your work and explain how you used the product rule of integer exponents
The product rule of integer exponents states that if you have a base raised to multiple exponents, you can multiply the exponents and keep the same base.
In this case, we have 12 raised to the exponent of -5 multiplied by 127.
To apply the product rule of integer exponents, we multiply -5 and 127 together and keep the base 12:
12^(-5) * 127 = 12^(-5 * 127)
Now we need to compute -5 * 127:
-5 * 127 = -635
So, the expression simplifies to:
12^(-635)
Now, we can calculate the numerical equivalent of 12^(-635) using a calculator.
The value of 12^(-635) is approximately 4.564939162e-618, where "e" is the scientific notation for "times 10 raised to the power of".
whats 12−5⋅127
To solve the expression 12^(-5) * 127, we need to evaluate each part separately.
First, let's calculate 12^(-5):
12^(-5) = 1 / 12^5 = 1 / (12*12*12*12*12) = 1 / 248,832 ≈ 0.00000403
Next, multiply this result by 127:
0.00000403 * 127 ≈ 0.00051281
Therefore, the numerical equivalent of 12^(-5) * 127 is approximately 0.00051281.
To apply the product rule of integer exponents, we can multiply the base and add the exponents. Let's break down the expression step by step:
Step 1: Start with the base, which is 12.
Step 2: Apply the product rule by multiplying the base (12) and adding the exponents (-5 and 7).
12^(-5) * 12^7 = 12^(-5+7) = 12^2
Step 3: Simplify the expression 12^2, which means multiplying 12 by itself.
12 × 12 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.
To find the numerical equivalent of 12^(-5) * 127 using the product rule of integer exponents, we need to understand the rule itself.
The product rule states that when you have the product of two numbers with the same base raised to different exponents, you can multiply the base and add the exponents. Mathematically, it can be represented as:
a^m * a^n = a^(m + n)
Now let's apply this rule to our expression: 12^(-5) * 127.
First, we can rewrite 12 as a base with an exponent of 1:
12^(-5) * 127 = (2 * 2 * 3)^(-5) * 127
Now we can expand the exponents using the product rule:
(2 * 2 * 3)^(-5) * 127 = 2^(-5) * 2^(-5) * 3^(-5) * 127
Since all the bases are the same (2, in this case), we can combine the exponents by adding them:
2^(-5) * 2^(-5) * 3^(-5) * 127 = 2^(-5 + -5) * 3^(-5) * 127
Simplifying the exponent:
2^(-10) * 3^(-5) * 127
Now, we can evaluate each part separately:
2^(-10) is equivalent to 1 / 2^10 = 1 / 1024
3^(-5) is equivalent to 1 / 3^5 = 1 / 243
So the numerical equivalent of 12^(-5) * 127 is:
(1 / 1024) * (1 / 243) * 127
Evaluating the expression:
(1 / 1024) * (1 / 243) * 127 = 0.0001144409
Therefore, the numerical equivalent of 12^(-5) * 127 is approximately 0.0001144409.